Iterated Shimura integrals

In this paper I continue the study of iterated integrals of modular forms and noncommutative modular symbols for $\mathrm{\Gamma }\subset SL(2,\mathbf{Z})$ started in [Ma3]. Main new results involve a description of the iterated Shimura cohomology and the image of the iterated Shimura cocycle class inside it. The concluding section of the paper contains a concise review of the classical modular symbols for SL(2) and a discussion of open problems.